Taylor series expansions for the entropy rate of Hidden Markov Processes

Abstract

Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this paper we generalize and prove a previous conjecture relating the entropy rate to entropies of finite systems. Building on our new theorems, we establish series expansions for the entropy rate in two different regimes. We also study the radius of convergence of the two series expansions.

References in corpus (1)

• The Entropy of a Binary Hidden Markov Process

Cited by in corpus (7)

• From finite-system entropy to entropy rate for a Hidden Markov Process
• The entropy rate of the binary symmetric channel in the rare transitions regime
• A Randomized Approach to the Capacity of Finite-State Channels
• Derivatives of Entropy Rate in Special Families of Hidden Markov Chains
• Limit Theorems in Hidden Markov Models
• Analyticity of Entropy Rate of Hidden Markov Chains
• Ziv-Merhav estimation for hidden-Markov processes